At least 16 more herb gardens must be sold in order to meet the fundraising goal
It is given that the environmental club is selling indoor herb gardens for $8 each for Earth Day.
The goal for the club is to raise at least $500 during the fundraiser.
So far the club has raised $256 toward the goal.
Let the number of herb gardens yet to be sold be 'x'
Thus total amount raised by 'x' herb garden sold= 8x
Thus, the equation for fundraising will be
8x+256=500
8x=500-256
8x=244
x= 244/8=31/2=15.5
Hence at least 16 more herb gardens must be sold in order to meet the fundraising goal
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Main Answer :16
Concept and definitions should be there:
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
a ≠ b says that a is not equal to b
a < b says that a is less than b
a > b says that a is greater than b
(those two are known as strict inequality)
a ≤ b means that a is less than or equal to b
a ≥ b means that a is greater than or equal to b.
Given that:
It is given that the environmental club is selling indoor herb gardens for $8 each for Earth Day.
The goal for the club is to raise at least $500 during the fundraiser.
So far the club has raised $256 toward the goal.
Solving Part:
Let the number of herb gardens yet to be sold be 'x'
Thus total amount raised by 'x' herb garden sold= 8x
I can match an inequality to a situation it represents, solve it, and then explain what the solution means in the situation.
If I have a situation and an inequality that represents it, I can explain what the parts of the inequality mean in the situation.
We know that
$256≥ $500 → inequality that represent the situation
Thus, the equation for fundraising will be
8x+256=500
8x=500-256
8x=244
x= 244/8=31/2=15.5
Hence at least 16 more herb gardens must be sold in order to meet the fundraising goal.
Final Answer: 16
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If p and q are negative integers such that [tex]p^2 \ \textgreater \ q^2[/tex],
then [tex]p^3[/tex] ________ [tex]q^3\\[/tex].
a) >
b) <
c) =
d) none of these
By compatibility principle of inequalities we complete the following sentence:
If p and q are negative integers such that p² > q², then p³ < q³. (Correct choice: B)
What is the relationship between two distinct negative integers?
According to the statement, the elements p and q are negative integers such that p² > q². By the sign law, the product of two negative numbers is always equal to a positive number, then by compatibility principle:
p² > q² Given
p · p > q · q Definition of power
p < q Compatibility principle
p³ < q³ Compatibility principle / Result
Please notice that the inequality symbol, that is, from "<" to ">" and viceversa, changes when the compatibility principle is applied in the given inequality.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of this function:
h(x) = (x − 1)2 − 9.
See attachment for the graph of the function and the features
How to use the drawing tool(s) to form the correct answer on the provided graph?The function is given as
h(x) =(x - 1)^2 - 9
The x-intercept
Set h(x) to 0
So, we have
(x - 1)^2 - 9 = 0
Add 9 to both sides
(x - 1)^2 = 9
Take the square root of both sides
x - 1 = ±3
This gives
x = 1 ± 3
Expand
x = (1 - 3, 1 + 3)
Evaluate
x = (-2, 4)
Hence, the x-intercepts are x =2 and x = 4
The y-intercept
Set x to 0
So, we have
h(0) = (0 - 1)^2 - 9
Evaluate
h(0) = -8
Hence, the y-intercept is h(x) =-8
The vertex
We have
h(x) =(x - 1)^2 - 9
Expand
h(x) = x^2 - 2x + 1 - 9
Differentiate
h'(x) = 2x - 2
Set to 0 and solve for x
2x - 2 = 0
This gives
x = 1 --- this represents the axis of symmetry
Substitute x = 1 in h(x) =(x - 1)^2 - 9
h(1) =(1 - 1)^2 - 9
Evaluate
h(1) = -9
Hence, the vertex of the function is (1, -9)
See attachment for the graph of the function and the features
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if 5 out of 30 students scored an A on a quiz.what percent did not get an A on the quiz?Round to the nearest whole percent.
PLEASE SHOW WORK
Answer:
83 %
Step-by-step explanation:
If 5 out of 30 got an A, that means that
30 -5 = 25
25 out of 30 did not get and A
25/30 = .8333333 = 83.33333 %
Rounding to the nearest whole percent
83 %
given that $a$ is an odd multiple of $7767$, find the greatest common divisor of $6a^2 49a 108$ and $2a 9$.
Odd Multiples of 7767 are 1, 3, 9, 863, 2589, 7767.The greatest common divisor of [tex]$6a^2 49a 108$[/tex] = 6×1×49×1×108= 31,752 and
2a9=2×1×9=18
What do you mean by Greatest Common Divisor?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor (GCD) in mathematics. The greatest common divisor of two numbers x and y is shown for x and y. As an illustration, the GCD of 8 and 12 equals 4, or. The words "divisor" and "factor" can be swapped out in the name "largest common divisor" so that alternative names such as "highest common factor" (HCF), etc. can be used instead. In the past, the term biggest common measure has been used to refer to the same idea.
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The price of an item has been reduced by $6.18. The new sale price is $30.55. What was the original price?
Answer:
30.55 + 6.18 = $36.73
Step-by-step explanation:
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What is P(AC)? I don’t know the answer to this
P(ac) means that it's 100%
A pharmacist mixes 5g of a power with 45cm of water to make a prescription medicine . how much powder should she mix with 81cm of water to make a larger amount of the same medicine.
The pharmacist should mix 9 g of a power to make a larger amount of the medicine
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
mass(1) = 5gvolume(1) = 45 cm3volume(2)= 81 cm3mass(2) = ?Calculating the rate of the medicine with the 1st mixed:
rate = mass(1)/ volume(1)
rate = 5g / 45cm3
rate = 0.11 g/cm3
Calculating how much power the pharmacist needs for the volume(2):
mass(2) = rate * volume(2)
mass(2) = 0.11 g/cm3 * 81 cm3
mass(2) = 9 g
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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A gasoline pump fills an automobile tank at the rate of .7 gallon every 2 seconds. At this rate, how long would it take to fill a 28- gallon tank?
Help!!
Answer:
80 seconds
Step-by-step explanation:
rate x time = gallons
[tex]\frac{.7}{2}[/tex]t = 28 Multiply both sides by [tex]\frac{2}{.7}[/tex]
t = 80
Lynden's first two, 100-meter-dash times are 13.075 seconds and 12.55 seconds. what are her mean (average) time? round your answer to the thousandths place.
The average time of Lynden's first two, 100-meter-dash is 12.813 seconds.
We are given the 100-meter-dash times of Lynden in first two races. So, the average time for first two races will be calculated using the formula -
Average = sum of all observations ÷ total number of observations
Sum of all observations here will be the sum of time of race.
Sum of observations = 13.075 + 12.55
Performing addition
Sum of observations = 25.625 seconds
Number of observations is the number of races whose time is taken in calculation.
Number of observations = 2
Keep the values in formula to find the average time.
Average time = 25.625 ÷ 2
Average time = 12.8125 seconds.
Rounding to nearest thousands place : 12.813 seconds
Hence, the average time of Lynden's first two, 100-meter-dash is 12.813 seconds.
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The Clear-Bell Cell phone company has a plan that costs
customers $29.99 for a monthly service fee plus 3¢ per minute used.
a. Write a linear equation to model this situation.
b. Identify the slope and the y-intercept. Interpret the slope and y-intercept in the context of this problem.
c. If Polly talks for 136 minutes, how much would her cell phone bill be (excluding taxes)?
Answer: a. y=0.03x+29.99
b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.
y-int: (0, 29.99). Total cost per month when phone isn't being used.
c. $34.07
Step-by-step explanation:
a. p=Cell phone plan. m=minutes used for phone.
3¢=$0.03
p=29.99+0.03m
y=0.03x+29.99
b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.
y=0.03(0)+29.99
p=29.99 ==> y-int: (0, 29.99). Total cost per month when phone isn't being used.
c. y=0.03(136)+29.99
y=4.08+29.99
y=$34.07
Find the surface area of a cube with side length og 6 1/2 inches.
PLEASE SHOW WORK
The surface area of a cube with side length of 6 1/2 inches is 253.5 square in
Surface area of cubeThe formula for calculating the surface area of cube is expressed as:
Surface area = 6L^2
where
L is the side length of the cube
Substitute
SA = 6(13/2)^2
SA = 6 * 169/4
SA = 3 * 169/2
SA = 253.5 square in
Hence the surface area of a cube with side length of 6 1/2 inches is 253.5 square in
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1. A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head
speed was 99 miles per hour. Was the baseball faster than the club head?
The baseball was faster than the club head will be incorrect.
What is conversion?Conversion means to convert the same thing into different units.
A baseball pitch traveled 128 feet per second. During a golfer's drive, the club head speed was 99 miles per hour.
We know that in one mile, there are 5280 feet. And in one hour, there are 3600 seconds.
Then the speed of the golfer's drive will be
⇒ 99 x 5280 feet / 3600 seconds
⇒ 145.2 feet per second
The speed of the club head is faster than the baseball.
The baseball was faster than the club head will be incorrect.
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16 divided by 200 times 100
[tex]16 : (200 \cdot 100) =[/tex]
[tex]16 : 20000 = 0.0008[/tex]
Answer:
8
Step-by-step explanation:
To solve this problem we use PEMDAS; Parenthesis, Exponents, Multiply, divide, add, subtract
Let's set up an equation:
16/200*100
Now let's solve:
16/200=0.08
Now we multiply 0.08 by 100
0.08*100=8
Thus, our answer is 8
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89 degrees
Step-by-step explanation:Triangles will always have 180 degrees. This means that given 2 angles, we can find the missing measurement.
Setting Up an Equation
To help us solve for the unknown angle, a, we can set up an algebraic equation. To make this equation remember that all 3 internal angles sum to 180.
14 + 77 + a = 180This is only one equation that you could set up to represent this situation.
Solving For a
Now that we have an equation we can begin to solve it. First, combine like terms that are on the same side of the equation.
91 + a = 180Next, subtract 91 from both sides.
a = 89To check our answer we can plug it back into the original equation.
14 + 77 + 89 = 180180 = 180This means that the missing angle must be 89 degrees.
Triangle ABC has the following angle measures:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
What is m∠A?
pleaseee help
The measure of angle A in the triangle is 18°
How to determine the measure of angle A?The angles in the triangle are given as:
m∠A = (2x − 24)°, m∠B = (x + 8)°, m∠C = (4x + 49)°
The sum of angles in a triangle is 180
So, we have
m∠A + m∠B + m∠C = 180
Substitute the known values in the above equation
So, we have:
2x − 24 + x + 8 + 4x + 49 = 180
Evaluate the like terms
7x = 147
Divide both sides by 7
x = 21
Substitute x = 21 in m∠A = (2x − 24)°
m∠A = (2 * 21 − 24)°
Evaluate
m∠A = 18°
Hence, the measure of angle A in the triangle is 18°
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Calculus help please
Step-by-step explanation:
THE POINT WHERE
[tex]f( - 4) = ( { - 4})^{2} + 1 \\ f( - 4) = 16 + 1 \\ f( - 4) = 17[/tex]
Now we have point (-4,17)
the gradient of the tangent line at that point of f(x) is the first derivative f'(x)=2x at that point
f'(x) =m
f'(-4)=2(-4)
f'(-4)=-8
The gradient therefore is -8
the general equation of a straight line is given by
[tex]y = mx + c \\ 17 = ( - 8)( - 4) + c \\ 17 = 32 + c \\ c = 17 - 32 \\ c = - 15 \\ \\ y = - 8x - 15[/tex]
HOPE THIS HELPS!!
your bedroom sock drawer contains 4 green socks and 6 yellow socks that are mixed together. the light in your room is broken so you must select your socks in the dark. what is the probability you will select two socks of the same color on your first try?
The probability of selecting two socks of same color is 0.96.
According to the given question.
Total number of green socks = 4
Total number of yellow socks = 6
So, the total number of socks in a drawer = 4 + 6 = 10
Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.
So, the probability of selecting a green scoks = 4/10 = 2/5
And the probability of selecting a yellow socks = 6/10 = 3/5
Therefore, the probability of selecting two socks of same color
= probability of selecting both the green socks or probability of selecting both the yellow socks
= [( 2/5) + (2/5)] × [(3/5)+(3/5)]
= (4/5) × (6/5)
= 24/25
= 0.96
Hence, the probability of selecting two socks of same color is 0.96.
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write a ratio and sentence comparing the number of jeans bought to the cost
In words, the ratio of the number of jeans bought to the cost is four to thirty two.
How to write a ratio?
We are told that you just bought 4 pairs of jeans for $32.
Now, since you bought 4 pairs for a cost of $32, then we can say that the ratio to represent the number jeans per dollars is;
4 :32
Thus, writing this in words we can say that the ratio of the number of jeans bought to the cost is four to thirty two.
Alternatively, we can also express it as a fraction with numerator and denominator as 4/32.
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Complete question is;
You just bought 4 pairs of jeans for $32. write a ratio and sentence comparing the number of jeans bought to the cost
a tripod has three legs each of length 5 feet. when the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground. in setting up the tripod, the lower 1 foot of one leg breaks off. let $h$ be the height in feet of the top of the tripod from the ground when the broken tripod is set up. then $h$ can be written in the form $\frac{m}{\sqrt{n}}$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. find $\lfloor m \sqrt{n} \rfloor$. (the notation $\lfloor x \rfloor$ denotes the greatest integer that is less than or equal to $x$.)
The value of [m + √n] is 183.
We note that AO=3. From this we can derive that the side length of the equilateral is 3√3. We now use 3D coordinate geometry.A is (0, 0, 0), B is (3√3, 0, 0), C is ((3√3)/2, 9/2, 0), T is ((3√3)/2, 3/2, 4), and S is ((3√3)/10, 3/10, 4/5).We know three points of the SCB plane, so we can write out the equation for the plane. Plane SCB can be expressed as (4√3)x + 4y + 39z - 36 = 0.Applying the distance between a point and a plane formula(ax + by + cz + d)/(√(a² + b² +c²)Put T's coordinates in this in (x, y, z), and replace the values of a, b, c, and d with plane equation coefficients.We get the distance equal to 144/(√1585).A distance of the form m/(√n) is given to us.We have to calculate [m + √n] = [144 + √1585] = 183.To learn more about plane, visit :
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In a week, a man received a paycheck for $826.60. The withholding for taxes was $91.40. If he worked 34 hours in that week, what is his hourly pay rate?
Answer:
Step-by-step explanation:
natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. a radio tracker costs $650 and a gps tracker costs $1400. natalie wants to buy at least 9 radio trackers and more than 3 gps trackers. the following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of gps trackers. x ≥ 9 y > 3 650x 1400y ≤ 15000 which yellow shaded region corresponds to natalie's possible choices?
Natalie will choose 7 and 8 as the yellow-shaded region corresponds to Natalie's possible choices.
What do you mean by GPS?Even though it appears complex, 3-dimensional trilateration is a straightforward mathematical process that underlies GPS. It's critical to have a fundamental understanding of 2-D Trilateration, which is necessary to completely comprehend 3-D Trilateration. Similar principles apply to three-dimensional trilateration, however, spheres rather than circles are used. Here is how the Global Positioning System uses 3-D trilateration to pinpoint an object's precise location. When the first satellite sends a signal, the GPS receiver measures the distance between the two. Say the distance between the receiver and the satellite is 20 000 miles. This implies that the receiver might be located anywhere on the 20 000 km diameter green sphere's surface and in any direction.
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Identify the rule(s) of algebra illustrated by the statement. (Select all that apply.) 1 · (1 + x) = 1 + x
The rule(s) of algebra illustrated by the statement is the identity property of algebra
How to identify the rule(s) of algebra illustrated by the statement.?The statement is given as:
1 · (1 + x) = 1 + x
The identity property of algebra states that:
1 * a = a or a * 1 = a
In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x
This can be illustrated as
1 * a = a
The rule(s) of algebra that illustrates the above equation is the identity property of algebra
Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra
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In ΔUVW, w = 3 inches, ∠W=23° and ∠U=73°. Find the length of u, to the nearest 10th of an inch.
The length of u by using sine rule is 7.4 to the nearest 10th of an inch.
What is sine rule?In mathematics, sine rule is a trigonometric method which relates the angle and side of a triangle. We can say that by using the sine rule we can find the side of any triangle if we knows the angle and vice versa. This rule is also known as law of sines.
Formulas for sine rule:
If we have three sides a, b, c and angle say A, B and C respectively .Then sine rule is :
[tex]\frac{Sin A}{a} = \frac{Sin B}{ b} = \frac{Sin C}{c}[/tex]
In the given question,
Sine rule will be used to get the unknown side of the triangle.
According to the rule;
[tex]\frac{Sin U}{u} = \frac{Sin V}{ v} = \frac{Sin W}{w}[/tex]
Given w = 3 in, ∠W=23° and ∠U=73°, substitute into the equation above to get u we have;
we can write the eq. as
[tex]\frac{Sin U}{u} = \frac{Sin W}{w}[/tex]
[tex]= > u = \frac{w \ sinu}{sinw} \\\\= > u = \frac{3 sin73}{sin 23} \\\\= > u = \frac{2.87}{0.39}\\ \\= > u = 7.398 = 7.4[/tex]
Hence, length of u is 7.4 inches to the nearest 10th of an inch.
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I need help solving. Im stuck please help me.
Which of the following is not a rational number?
Α. 0
B. √2
C. 3/4
D. √4
Answer: B
Step-by-step explanation: the square root of 2 cannot really be expressed as a fraction where both the numerator and the denominator are integers.
Answer:
B
Step-by-step explanation:
How do we find the "rate of change"
Answer: To find the average rate of change, divide the change in y-values by the change in x-values
Step-by-step explanation:
Louis sets off a firework. The height of the firework at the time t seconds is given by h (t) 16t^2+128t.
Use the quadratic formula to estimate when into the trip the rocket is 64 feet high.
A
at about 0.4 seconds and about 7.6 seconds
B
at about 0.8 second and about 5.2 seconds
C
at about 1.1 seconds and about 6.8 seconds
D
at about 0.5 seconds and about 7.5 seconds
The option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.
What is a quadratic equation ?
A quadratic equation is an equation which contains a single variable of degree 2 and its general form is ax² + bx + c = 0.
The height of firework is represented by a quadratic equation which is 16t² + 128t.
Let's find out that at what time the rocket will be at height of 64 feet.
So,
16t² + 128t = 64 feet
or
16t² + 128t - 64 = 0
or
t² + 8t - 4 = 0
We know that quadratic equation is in form ax² + bx + c = 0.
Using the quadratic formula to find value of t :
[tex]t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
t = [ -8 ± √(8² - (4 × 1 × - 4))] / ( 2 × 1 )
t = [ - 8 ± 8.94 ] / 2
t = -4 ± 4.47
So , the value of t can be either -4 + 4.47 or -4 - 4.47 which is equal to 0.47 or - 8.47 seconds. Time can't be negative , so t = 0.47 or 0.5 seconds.
Therefore , the option D is correct that is at about 0.5 seconds and about 7.5 seconds the firework will be at height 64 feet.
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Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running
How to illustrate the information?From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.
The equation is
3w + 6r ≥ 36
3w + 6r ≤ 90
The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking; and 12 hours running.
This will be:
3w + 6r ≤ 90
3(2) + 6(12)
6 + 72 = 78
Therefore, 78 is less than 90.
The correct option is A.
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What transformation is represented by the rule
(1, y) → (1, y+3)?
O translation 3 units down
O translation 3 units right
O translation 3 units up
O translation 3 units left
X
. You deposit money in an account that earns Simple interest at an annual rate of 6%. After 8 years.
Y
the account earns $360 in interest. How much money did you deposit in the account?
Answer:
$750
Step-by-step explanation:
I = interest
p = principle
r = rate
t = time
I = prt Plug in what you know and solve for p
360 = p (.06)(8)
360 =p.48 Divide both sides by .48
750 = p
The principal is deposited in the account is $750.
Given that, rate of interest =6%, time period = 8 years and simple interest = $360.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 360 = (P×6×8)/100
⇒ 360 = 48P/100
⇒ 48P = 36000
⇒ P = 36000/48
⇒ P = $750
Therefore, the principal is deposited in the account is $750.
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